Prakash J.
asked • 03/20/17(x+y)³+4(x+y)²+4x+4y
How can solve the problem
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2 Answers By Expert Tutors
Andrew M. answered • 03/20/17
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
(x + y)3 = x3 + y3 + 3xy(x + y)
= x3 + y3 + 3x2y + 3xy2
(x+y)2 = x2 + 2xy + y2
4(x+y)2 = 4x2 + 8xy + 4y2
(x+y)³+4(x+y)²+4x+4y =
x3 + y3 + 3x2y + 3xy2 + 4x2 + 8xy + 4y2 + 4x + 4y
This is the expansion of the expression given.
What are you trying to determine?
Michael J. answered • 03/20/17
Tutor
5
(5)
Effective High School STEM Tutor & CUNY Math Peer Leader
The last two terms can be factored.
(x + y)3 + 4(x + y)2 + 4(x + y)
(x + y) is the GCF.
(x + y)[(x + y)2 + 4(x + y) + 4]
Let w = x + y
Then,
w(w2 + 4w + 4) =
w(w + 2)(w + 2) =
(x + y)((x + y) + 2)((x + y) + 2) =
(x + y)(x + y + 2)(x + y + 2)
Andrew M.
If we are trying to find the roots they occur at
w = 0 or w = -2
x+y = 0
x = -y
x+y = -2
x = -2 - y
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03/20/17
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Andrew M.
03/20/17